The theory behind CVA

The function means()

  • This function controls the aesthetics of the class means in the biplot
  • Apply these aesthetics through arguments

Deciding which of the means to plot

biplot(state.x77) |> CVA(state.region) |> means(which = c(2,3)) |> plot()

Colours and characters for the points

biplot(state.x77) |> CVA(state.region) |> means(cex = c(1,2,3,4),col = "red",pch = c(9,13,4,16)) |> plot()

Labels

biplot(state.x77) |> CVA(state.region) |> means(label = TRUE,label.side = "top",label.offset = 2,label.cex = 1) |> plot()

The function classify()

This function deals with classification regions \ The classify() function appends the biplot object with the following elements: \ - A confusion matrix from the classification into classes - The classification accuracy rate - A logical value indicating whether classification regions are shown in the biplot - A list of chosen aesthetics for the classification regions - The midpoints of the classification regions

class.examp<-biplot(state.x77) |> CVA(state.region) |> classify(col = c("cornflowerblue","darkolivegreen3","darkgoldenrod","aquamarine"))
class.examp$classify
# $table
#                Reference
# Prediction      Northeast South North Central West
#   Northeast             8     0             1    0
#   South                 1    15             0    0
#   North Central         1     1            10    0
#   West                  0     0             0   13
# 
# $rate
# Accuracy 
#     0.92 
# 
# $classify.regions
# [1] TRUE
# 
# $region.midpoints
#                      [,1]        [,2]
# Northeast      0.12052780 -0.26463306
# South         -0.33825365  0.07559722
# North Central  0.07533527 -0.17178605
# West           0.26332961  0.24873651
# 
# $aes
# $aes$col
# [1] "#6495ED66" "#A2CD5A66" "#B8860B66" "#7FFFD466"
# 
# $aes$opacity
# [1] 0.4
# 
# $aes$borders
# [1] FALSE
class.examp |> plot()

The function alpha.bags()

This function creates \(\alpha\)-bags \ The alpha.bags() function appends the biplot object with the following elements: \ - A list of coordinates for the \(\alpha\)-bags for each group - A vector of colours for the \(\alpha\)-bags - A vector of line types for the \(\alpha\)-bags - A vector of line widths for the \(\alpha\)-bags

ab.examp<-biplot(state.x77) |> CVA(state.region) |> alpha.bags(alpha = c(0.85,0.9,0.95,0.99),lty = c(1,2,3,4))
# Computing 0.85 -bag for Northeast 
# Computing 0.9 -bag for South 
# Computing 0.95 -bag for North Central 
# Computing 0.99 -bag for West
ab.examp$alpha.bags
# $`Northeast-0.85`
#              [,1]        [,2]
#  [1,]  0.16633269 -0.34121856
#  [2,]  0.08880408 -0.38102939
#  [3,]  0.04707484 -0.39691735
#  [4,]  0.04262374 -0.39694881
#  [5,]  0.01983496 -0.39710802
#  [6,] -0.08658833 -0.37469874
#  [7,] -0.08658829 -0.37469774
#  [8,]  0.09848353 -0.15078535
#  [9,]  0.16580200 -0.07804116
# [10,]  0.19860357 -0.10560387
# [11,]  0.26022465 -0.17946223
# [12,]  0.26351202 -0.18511612
# [13,]  0.26351247 -0.18511719
# [14,]  0.26668494 -0.20058334
# [15,]  0.26668476 -0.20058463
# [16,]  0.24892584 -0.22957517
# 
# $`South-0.9`
#           [,1]         [,2]
#    -0.04734292  0.036516134
#    -0.04734302  0.036514770
#    -0.09992945 -0.015024416
#    -0.14927508 -0.051432512
#    -0.22354495 -0.077942971
#    -0.36599759 -0.117362800
#    -0.48735239 -0.094678439
#    -0.49976670 -0.091177816
#    -0.50438984 -0.088476626
# sl -0.51619403 -0.075945622
# sl -0.52200140  0.005174029
#    -0.52218463  0.011746394
#    -0.52497645  0.129443574
#    -0.52222437  0.325730381
#    -0.52222433  0.325731539
#    -0.36858212  0.296091464
#    -0.36027380  0.293499192
#    -0.34582110  0.288915878
#    -0.19220404  0.227718399
#    -0.13009266  0.158795901
#    -0.07507638  0.091283070
#    -0.07507559  0.091281684
# 
# $`North Central-0.95`
#              [,1]         [,2]
#  [1,]  0.24022097 -0.121798637
#  [2,]  0.24041247 -0.124853201
#  [3,]  0.24198566 -0.149997207
#  [4,]  0.24198571 -0.149998765
#  [5,]  0.23824746 -0.268840097
#  [6,]  0.23824740 -0.268841560
#  [7,]  0.17747475 -0.327065706
#  [8,]  0.01269478 -0.468235431
#  [9,] -0.13241334 -0.165868998
# [10,] -0.20722221  0.005971102
# [11,] -0.20722222  0.005972554
# [12,] -0.11418651  0.022533061
# [13,] -0.06574489  0.028766686
# [14,]  0.03116764  0.041193137
# [15,]  0.18315932  0.051420222
# [16,]  0.22798305 -0.040029586
# [17,]  0.23609112 -0.060956142
# 
# $`West-0.99`
#          [,1]       [,2]
# sr 0.40944473 0.09343949
# sr 0.40064366 0.08212953
#    0.38322828 0.06051974
#    0.36382821 0.06015583
#    0.35085860 0.06002291
#    0.33792742 0.06007482
#    0.32212424 0.06450568
#    0.32024851 0.06503188
#    0.28759382 0.07446779
#    0.21595645 0.09575543
#    0.17883496 0.14824762
# sl 0.10634397 0.25255297
# sl 0.08153650 0.28871482
# sl 0.08153649 0.28871637
# sl 0.08404261 0.36108532
#    0.08659044 0.41386061
#    0.08694699 0.42055496
#    0.10654148 0.43414262
#    0.13067615 0.45058965
#    0.35702476 0.60138841
#    0.46904566 0.33475158
#    0.50543483 0.24615210
# sr 0.51318505 0.22695613
# sr 0.51318505 0.22695458
ab.examp |> plot()

The function ellipses()

This function creates \(\kappa\)-ellipses \ The alpha.bags() function appends the biplot object with the following elements: \ - A list of coordinates for the \(\kappa\)-bags for each group - A vector of colours for the \(\kappa\)-bags - A vector of line types for the \(\kappa\)-bags - A vector of line widths for the \(\kappa\)-bags - A vector of \(\alpha\) values

kc.examp<-biplot(state.x77) |> CVA(state.region) |> ellipses(alpha = c(0.85,0.9,0.95,0.99),lwd = c(1,2,3,4))
# Computing 1.95 -ellipse for Northeast 
# Computing 2.15 -ellipse for South 
# Computing 2.45 -ellipse for North Central 
# Computing 3.03 -ellipse for West
kc.examp$conc.ellipses
# $`Northeast-1.95`
#                 [,1]        [,2]
#   [1,] -0.1104009263 -0.48947500
#   [2,] -0.1113637518 -0.48846301
#   [3,] -0.1123033884 -0.48742863
#   [4,] -0.1132197420 -0.48637198
#   [5,] -0.1141127211 -0.48529315
#   [6,] -0.1149822363 -0.48419226
#   [7,] -0.1158282008 -0.48306941
#   [8,] -0.1166505298 -0.48192472
#   [9,] -0.1174491412 -0.48075829
#  [10,] -0.1182239550 -0.47957026
#  [11,] -0.1189748939 -0.47836073
#  [12,] -0.1197018828 -0.47712983
#  [13,] -0.1204048488 -0.47587768
#  [14,] -0.1210837219 -0.47460441
#  [15,] -0.1217384339 -0.47331014
#  [16,] -0.1223689195 -0.47199500
#  [17,] -0.1229751157 -0.47065913
#  [18,] -0.1235569618 -0.46930265
#  [19,] -0.1241143996 -0.46792571
#  [20,] -0.1246473734 -0.46652844
#  [21,] -0.1251558298 -0.46511097
#  [22,] -0.1256397182 -0.46367346
#  [23,] -0.1260989899 -0.46221605
#  [24,] -0.1265335992 -0.46073888
#  [25,] -0.1269435026 -0.45924210
#  [26,] -0.1273286590 -0.45772586
#  [27,] -0.1276890300 -0.45619030
#  [28,] -0.1280245796 -0.45463560
#  [29,] -0.1283352741 -0.45306189
#  [30,] -0.1286210824 -0.45146934
#  [31,] -0.1288819762 -0.44985811
#  [32,] -0.1291179291 -0.44822835
#  [33,] -0.1293289177 -0.44658023
#  [34,] -0.1295149208 -0.44491392
#  [35,] -0.1296759199 -0.44322959
#  [36,] -0.1298118988 -0.44152739
#  [37,] -0.1299228439 -0.43980750
#  [38,] -0.1300087442 -0.43807010
#  [39,] -0.1300695910 -0.43631535
#  [40,] -0.1301053783 -0.43454344
#  [41,] -0.1301161025 -0.43275453
#  [42,] -0.1301017625 -0.43094881
#  [43,] -0.1300623598 -0.42912646
#  [44,] -0.1299978982 -0.42728766
#  [45,] -0.1299083843 -0.42543260
#  [46,] -0.1297938270 -0.42356145
#  [47,] -0.1296542377 -0.42167442
#  [48,] -0.1294896305 -0.41977167
#  [49,] -0.1293000217 -0.41785342
#  [50,] -0.1290854303 -0.41591984
#  [51,] -0.1288458778 -0.41397114
#  [52,] -0.1285813882 -0.41200750
#  [53,] -0.1282919878 -0.41002912
#  [54,] -0.1279777057 -0.40803621
#  [55,] -0.1276385732 -0.40602895
#  [56,] -0.1272746243 -0.40400756
#  [57,] -0.1268858954 -0.40197222
#  [58,] -0.1264724253 -0.39992316
#  [59,] -0.1260342554 -0.39786056
#  [60,] -0.1255714294 -0.39578464
#  [61,] -0.1250839938 -0.39369561
#  [62,] -0.1245719972 -0.39159367
#  [63,] -0.1240354908 -0.38947904
#  [64,] -0.1234745283 -0.38735192
#  [65,] -0.1228891658 -0.38521253
#  [66,] -0.1222794617 -0.38306108
#  [67,] -0.1216454772 -0.38089778
#  [68,] -0.1209872755 -0.37872287
#  [69,] -0.1203049225 -0.37653654
#  [70,] -0.1195984865 -0.37433902
#  [71,] -0.1188680380 -0.37213053
#  [72,] -0.1181136501 -0.36991130
#  [73,] -0.1173353983 -0.36768153
#  [74,] -0.1165333604 -0.36544146
#  [75,] -0.1157076165 -0.36319131
#  [76,] -0.1148582493 -0.36093130
#  [77,] -0.1139853437 -0.35866167
#  [78,] -0.1130889870 -0.35638263
#  [79,] -0.1121692688 -0.35409441
#  [80,] -0.1112262811 -0.35179725
#  [81,] -0.1102601181 -0.34949138
#  [82,] -0.1092708766 -0.34717701
#  [83,] -0.1082586554 -0.34485440
#  [84,] -0.1072235557 -0.34252376
#  [85,] -0.1061656811 -0.34018533
#  [86,] -0.1050851373 -0.33783935
#  [87,] -0.1039820325 -0.33548605
#  [88,] -0.1028564768 -0.33312566
#  [89,] -0.1017085829 -0.33075842
#  [90,] -0.1005384655 -0.32838457
#  [91,] -0.0993462417 -0.32600434
#  [92,] -0.0981320307 -0.32361798
#  [93,] -0.0968959538 -0.32122572
#  [94,] -0.0956381348 -0.31882780
#  [95,] -0.0943586994 -0.31642446
#  [96,] -0.0930577755 -0.31401594
#  [97,] -0.0917354932 -0.31160249
#  [98,] -0.0903919848 -0.30918433
#  [99,] -0.0890273845 -0.30676172
# [100,] -0.0876418289 -0.30433490
# [101,] -0.0862354566 -0.30190411
# [102,] -0.0848084080 -0.29946959
# [103,] -0.0833608261 -0.29703159
# [104,] -0.0818928554 -0.29459035
# [105,] -0.0804046428 -0.29214611
# [106,] -0.0788963372 -0.28969912
# [107,] -0.0773680893 -0.28724962
# [108,] -0.0758200520 -0.28479786
# [109,] -0.0742523801 -0.28234409
# [110,] -0.0726652303 -0.27988855
# [111,] -0.0710587614 -0.27743148
# [112,] -0.0694331339 -0.27497312
# [113,] -0.0677885106 -0.27251374
# [114,] -0.0661250557 -0.27005357
# [115,] -0.0644429358 -0.26759285
# [116,] -0.0627423189 -0.26513184
# [117,] -0.0610233752 -0.26267078
# [118,] -0.0592862764 -0.26020992
# [119,] -0.0575311965 -0.25774950
# [120,] -0.0557583108 -0.25528976
# [121,] -0.0539677966 -0.25283096
# [122,] -0.0521598330 -0.25037334
# [123,] -0.0503346008 -0.24791715
# [124,] -0.0484922825 -0.24546263
# [125,] -0.0466330623 -0.24301003
# [126,] -0.0447571262 -0.24055958
# [127,] -0.0428646617 -0.23811155
# [128,] -0.0409558581 -0.23566617
# [129,] -0.0390309063 -0.23322368
# [130,] -0.0370899987 -0.23078433
# [131,] -0.0351333295 -0.22834837
# [132,] -0.0331610943 -0.22591604
# [133,] -0.0311734904 -0.22348758
# [134,] -0.0291707165 -0.22106324
# [135,] -0.0271529728 -0.21864325
# [136,] -0.0251204611 -0.21622786
# [137,] -0.0230733848 -0.21381731
# [138,] -0.0210119485 -0.21141184
# [139,] -0.0189363583 -0.20901169
# [140,] -0.0168468218 -0.20661711
# [141,] -0.0147435480 -0.20422833
# [142,] -0.0126267471 -0.20184559
# [143,] -0.0104966309 -0.19946912
# [144,] -0.0083534124 -0.19709918
# [145,] -0.0061973058 -0.19473598
# [146,] -0.0040285269 -0.19237978
# [147,] -0.0018472924 -0.19003080
# [148,]  0.0003461795 -0.18768928
# [149,]  0.0025516695 -0.18535546
# [150,]  0.0047689569 -0.18302956
# [151,]  0.0069978202 -0.18071183
# [152,]  0.0092380363 -0.17840248
# [153,]  0.0114893814 -0.17610176
# [154,]  0.0137516302 -0.17380990
# [155,]  0.0160245565 -0.17152711
# [156,]  0.0183079330 -0.16925364
# [157,]  0.0206015315 -0.16698970
# [158,]  0.0229051225 -0.16473553
# [159,]  0.0252184757 -0.16249134
# [160,]  0.0275413597 -0.16025737
# [161,]  0.0298735423 -0.15803384
# [162,]  0.0322147903 -0.15582097
# [163,]  0.0345648694 -0.15361898
# [164,]  0.0369235448 -0.15142809
# [165,]  0.0392905806 -0.14924852
# [166,]  0.0416657400 -0.14708049
# [167,]  0.0440487856 -0.14492421
# [168,]  0.0464394789 -0.14277991
# [169,]  0.0488375811 -0.14064779
# [170,]  0.0512428522 -0.13852807
# [171,]  0.0536550518 -0.13642096
# [172,]  0.0560739386 -0.13432667
# [173,]  0.0584992707 -0.13224541
# [174,]  0.0609308056 -0.13017739
# [175,]  0.0633683001 -0.12812281
# [176,]  0.0658115106 -0.12608189
# [177,]  0.0682601926 -0.12405482
# [178,]  0.0707141014 -0.12204181
# [179,]  0.0731729915 -0.12004306
# [180,]  0.0756366170 -0.11805876
# [181,]  0.0781047316 -0.11608913
# [182,]  0.0805770885 -0.11413435
# [183,]  0.0830534404 -0.11219461
# [184,]  0.0855335397 -0.11027013
# [185,]  0.0880171384 -0.10836107
# [186,]  0.0905039882 -0.10646765
# [187,]  0.0929938403 -0.10459004
# [188,]  0.0954864458 -0.10272844
# [189,]  0.0979815554 -0.10088302
# [190,]  0.1004789196 -0.09905398
# [191,]  0.1029782887 -0.09724150
# [192,]  0.1054794127 -0.09544576
# [193,]  0.1079820415 -0.09366693
# [194,]  0.1104859249 -0.09190521
# [195,]  0.1129908125 -0.09016075
# [196,]  0.1154964538 -0.08843374
# [197,]  0.1180025982 -0.08672435
# [198,]  0.1205089951 -0.08503276
# [199,]  0.1230153939 -0.08335912
# [200,]  0.1255215440 -0.08170361
# [201,]  0.1280271946 -0.08006639
# [202,]  0.1305320954 -0.07844763
# [203,]  0.1330359957 -0.07684749
# [204,]  0.1355386452 -0.07526613
# [205,]  0.1380397937 -0.07370370
# [206,]  0.1405391909 -0.07216036
# [207,]  0.1430365870 -0.07063628
# [208,]  0.1455317323 -0.06913159
# [209,]  0.1480243772 -0.06764645
# [210,]  0.1505142725 -0.06618101
# [211,]  0.1530011691 -0.06473541
# [212,]  0.1554848184 -0.06330981
# [213,]  0.1579649721 -0.06190434
# [214,]  0.1604413821 -0.06051914
# [215,]  0.1629138007 -0.05915435
# [216,]  0.1653819808 -0.05781011
# [217,]  0.1678456755 -0.05648655
# [218,]  0.1703046384 -0.05518380
# [219,]  0.1727586237 -0.05390200
# [220,]  0.1752073860 -0.05264128
# [221,]  0.1776506804 -0.05140175
# [222,]  0.1800882625 -0.05018354
# [223,]  0.1825198886 -0.04898678
# [224,]  0.1849453155 -0.04781159
# [225,]  0.1873643008 -0.04665807
# [226,]  0.1897766025 -0.04552636
# [227,]  0.1921819793 -0.04441655
# [228,]  0.1945801908 -0.04332877
# [229,]  0.1969709971 -0.04226311
# [230,]  0.1993541592 -0.04121969
# [231,]  0.2017294386 -0.04019862
# [232,]  0.2040965980 -0.03919998
# [233,]  0.2064554006 -0.03822389
# [234,]  0.2088056105 -0.03727045
# [235,]  0.2111469926 -0.03633973
# [236,]  0.2134793130 -0.03543185
# [237,]  0.2158023382 -0.03454688
# [238,]  0.2181158361 -0.03368493
# [239,]  0.2204195753 -0.03284607
# [240,]  0.2227133253 -0.03203039
# [241,]  0.2249968569 -0.03123796
# [242,]  0.2272699417 -0.03046888
# [243,]  0.2295323524 -0.02972321
# [244,]  0.2317838627 -0.02900104
# [245,]  0.2340242474 -0.02830242
# [246,]  0.2362532827 -0.02762744
# [247,]  0.2384707454 -0.02697616
# [248,]  0.2406764140 -0.02634865
# [249,]  0.2428700678 -0.02574496
# [250,]  0.2450514875 -0.02516517
# [251,]  0.2472204549 -0.02460931
# [252,]  0.2493767532 -0.02407747
# [253,]  0.2515201667 -0.02356967
# [254,]  0.2536504810 -0.02308598
# [255,]  0.2557674832 -0.02262645
# [256,]  0.2578709615 -0.02219112
# [257,]  0.2599607057 -0.02178003
# [258,]  0.2620365066 -0.02139323
# [259,]  0.2640981568 -0.02103075
# [260,]  0.2661454501 -0.02069263
# [261,]  0.2681781818 -0.02037890
# [262,]  0.2701961485 -0.02008960
# [263,]  0.2721991485 -0.01982476
# [264,]  0.2741869815 -0.01958439
# [265,]  0.2761594487 -0.01936853
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# [513,]  0.1184393717 -0.44564166
# [514,]  0.1159331652 -0.44730007
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# [519,]  0.1034140352 -0.45531486
# [520,]  0.1009143423 -0.45686125
# [521,]  0.0984166107 -0.45838841
# [522,]  0.0959210902 -0.45989620
# [523,]  0.0934280304 -0.46138446
# [524,]  0.0909376806 -0.46285305
# [525,]  0.0884502897 -0.46430181
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# [528,]  0.0810083567 -0.46852774
# [529,]  0.0785352858 -0.46989579
# [530,]  0.0760664142 -0.47124331
# [531,]  0.0736019886 -0.47257017
# [532,]  0.0711422556 -0.47387624
# [533,]  0.0686874611 -0.47516138
# [534,]  0.0662378505 -0.47642547
# [535,]  0.0637936690 -0.47766839
# [536,]  0.0613551607 -0.47889000
# [537,]  0.0589225698 -0.48009018
# [538,]  0.0564961392 -0.48126882
# [539,]  0.0540761118 -0.48242579
# [540,]  0.0516627295 -0.48356099
# [541,]  0.0492562337 -0.48467429
# [542,]  0.0468568649 -0.48576559
# [543,]  0.0444648632 -0.48683478
# [544,]  0.0420804677 -0.48788174
# [545,]  0.0397039169 -0.48890638
# [546,]  0.0373354484 -0.48990860
# [547,]  0.0349752990 -0.49088829
# [548,]  0.0326237049 -0.49184535
# [549,]  0.0302809011 -0.49277969
# [550,]  0.0279471219 -0.49369121
# [551,]  0.0256226006 -0.49457983
# [552,]  0.0233075699 -0.49544546
# [553,]  0.0210022610 -0.49628800
# [554,]  0.0187069047 -0.49710738
# [555,]  0.0164217303 -0.49790352
# [556,]  0.0141469665 -0.49867632
# [557,]  0.0118828406 -0.49942572
# [558,]  0.0096295792 -0.50015165
# [559,]  0.0073874075 -0.50085402
# [560,]  0.0051565497 -0.50153277
# [561,]  0.0029372289 -0.50218782
# [562,]  0.0007296672 -0.50281913
# [563,] -0.0014659149 -0.50342661
# [564,] -0.0036492977 -0.50401022
# [565,] -0.0058202629 -0.50456989
# [566,] -0.0079785934 -0.50510556
# [567,] -0.0101240733 -0.50561719
# [568,] -0.0122564882 -0.50610472
# [569,] -0.0143756248 -0.50656810
# [570,] -0.0164812711 -0.50700729
# [571,] -0.0185732167 -0.50742225
# [572,] -0.0206512522 -0.50781292
# [573,] -0.0227151700 -0.50817928
# [574,] -0.0247647636 -0.50852128
# [575,] -0.0267998280 -0.50883889
# [576,] -0.0288201598 -0.50913208
# [577,] -0.0308255570 -0.50940082
# [578,] -0.0328158189 -0.50964509
# [579,] -0.0347907466 -0.50986486
# [580,] -0.0367501426 -0.51006010
# [581,] -0.0386938109 -0.51023080
# [582,] -0.0406215572 -0.51037694
# [583,] -0.0425331887 -0.51049850
# [584,] -0.0444285142 -0.51059548
# [585,] -0.0463073442 -0.51066787
# [586,] -0.0481694909 -0.51071565
# [587,] -0.0500147680 -0.51073882
# [588,] -0.0518429909 -0.51073738
# [589,] -0.0536539769 -0.51071133
# [590,] -0.0554475449 -0.51066068
# [591,] -0.0572235155 -0.51058542
# [592,] -0.0589817111 -0.51048557
# [593,] -0.0607219559 -0.51036113
# [594,] -0.0624440759 -0.51021212
# [595,] -0.0641478989 -0.51003855
# [596,] -0.0658332544 -0.50984044
# [597,] -0.0674999740 -0.50961781
# [598,] -0.0691478910 -0.50937068
# [599,] -0.0707768405 -0.50909908
# [600,] -0.0723866598 -0.50880303
# [601,] -0.0739771877 -0.50848257
# [602,] -0.0755482654 -0.50813772
# [603,] -0.0770997356 -0.50776852
# [604,] -0.0786314432 -0.50737500
# [605,] -0.0801432350 -0.50695722
# [606,] -0.0816349599 -0.50651520
# [607,] -0.0831064687 -0.50604899
# [608,] -0.0845576143 -0.50555864
# [609,] -0.0859882514 -0.50504420
# [610,] -0.0873982372 -0.50450572
# [611,] -0.0887874305 -0.50394325
# [612,] -0.0901556924 -0.50335685
# [613,] -0.0915028862 -0.50274658
# [614,] -0.0928288771 -0.50211249
# [615,] -0.0941335325 -0.50145466
# [616,] -0.0954167220 -0.50077315
# [617,] -0.0966783172 -0.50006802
# [618,] -0.0979181919 -0.49933935
# [619,] -0.0991362222 -0.49858721
# [620,] -0.1003322864 -0.49781168
# [621,] -0.1015062646 -0.49701282
# [622,] -0.1026580397 -0.49619073
# [623,] -0.1037874964 -0.49534548
# [624,] -0.1048945217 -0.49447717
# [625,] -0.1059790050 -0.49358586
# [626,] -0.1070408378 -0.49267167
# [627,] -0.1080799139 -0.49173467
# [628,] -0.1090961294 -0.49077496
# [629,] -0.1100893828 -0.48979263
# 
# $`South-2.15`
#                 [,1]          [,2]
#   [1,] -7.106971e-01  1.090893e-01
#   [2,] -7.104026e-01  1.121559e-01
#   [3,] -7.100708e-01  1.152188e-01
#   [4,] -7.097019e-01  1.182777e-01
#   [5,] -7.092958e-01  1.213324e-01
#   [6,] -7.088526e-01  1.243825e-01
#   [7,] -7.083724e-01  1.274277e-01
#   [8,] -7.078552e-01  1.304678e-01
#   [9,] -7.073009e-01  1.335023e-01
#  [10,] -7.067098e-01  1.365311e-01
#  [11,] -7.060819e-01  1.395537e-01
#  [12,] -7.054171e-01  1.425700e-01
#  [13,] -7.047157e-01  1.455796e-01
#  [14,] -7.039776e-01  1.485821e-01
#  [15,] -7.032029e-01  1.515774e-01
#  [16,] -7.023917e-01  1.545651e-01
#  [17,] -7.015441e-01  1.575449e-01
#  [18,] -7.006602e-01  1.605165e-01
#  [19,] -6.997401e-01  1.634796e-01
#  [20,] -6.987838e-01  1.664339e-01
#  [21,] -6.977914e-01  1.693791e-01
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# [590,] -6.928485e-01 -1.102219e-02
# [591,] -6.940028e-01 -8.055435e-03
# [592,] -6.951216e-01 -5.080317e-03
# [593,] -6.962046e-01 -2.097133e-03
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# [595,] -6.982633e-01  3.892246e-03
# [596,] -6.992387e-01  6.897841e-03
# [597,] -7.001780e-01  9.910306e-03
# [598,] -7.010811e-01  1.292934e-02
# [599,] -7.019479e-01  1.595464e-02
# [600,] -7.027783e-01  1.898590e-02
# [601,] -7.035723e-01  2.202283e-02
# [602,] -7.043298e-01  2.506511e-02
# [603,] -7.050506e-01  2.811245e-02
# [604,] -7.057348e-01  3.116453e-02
# [605,] -7.063822e-01  3.422106e-02
# [606,] -7.069928e-01  3.728173e-02
# [607,] -7.075666e-01  4.034622e-02
# [608,] -7.081034e-01  4.341424e-02
# [609,] -7.086032e-01  4.648548e-02
# [610,] -7.090660e-01  4.955964e-02
# [611,] -7.094917e-01  5.263639e-02
# [612,] -7.098803e-01  5.571544e-02
# [613,] -7.102317e-01  5.879648e-02
# [614,] -7.105459e-01  6.187920e-02
# [615,] -7.108229e-01  6.496329e-02
# [616,] -7.110627e-01  6.804845e-02
# [617,] -7.112651e-01  7.113436e-02
# [618,] -7.114303e-01  7.422071e-02
# [619,] -7.115581e-01  7.730720e-02
# [620,] -7.116486e-01  8.039353e-02
# [621,] -7.117018e-01  8.347937e-02
# [622,] -7.117176e-01  8.656442e-02
# [623,] -7.116961e-01  8.964838e-02
# [624,] -7.116372e-01  9.273093e-02
# [625,] -7.115410e-01  9.581177e-02
# [626,] -7.114075e-01  9.889059e-02
# [627,] -7.112367e-01  1.019671e-01
# [628,] -7.110285e-01  1.050409e-01
# [629,] -7.107831e-01  1.081118e-01
# 
# $`North Central-2.45`
#                [,1]          [,2]
#   [1,] -0.115309509  1.741007e-01
#   [2,] -0.112312272  1.757301e-01
#   [3,] -0.109296270  1.773248e-01
#   [4,] -0.106261806  1.788846e-01
#   [5,] -0.103209181  1.804094e-01
#   [6,] -0.100138703  1.818989e-01
#   [7,] -0.097050677  1.833530e-01
#   [8,] -0.093945412  1.847716e-01
#   [9,] -0.090823220  1.861546e-01
#  [10,] -0.087684412  1.875018e-01
#  [11,] -0.084529302  1.888130e-01
#  [12,] -0.081358206  1.900882e-01
#  [13,] -0.078171441  1.913272e-01
#  [14,] -0.074969325  1.925299e-01
#  [15,] -0.071752179  1.936962e-01
#  [16,] -0.068520324  1.948259e-01
#  [17,] -0.065274083  1.959190e-01
#  [18,] -0.062013782  1.969753e-01
#  [19,] -0.058739746  1.979947e-01
#  [20,] -0.055452303  1.989771e-01
#  [21,] -0.052151781  1.999225e-01
#  [22,] -0.048838511  2.008306e-01
#  [23,] -0.045512823  2.017016e-01
#  [24,] -0.042175050  2.025351e-01
#  [25,] -0.038825527  2.033313e-01
#  [26,] -0.035464587  2.040899e-01
#  [27,] -0.032092568  2.048110e-01
#  [28,] -0.028709806  2.054943e-01
#  [29,] -0.025316640  2.061400e-01
#  [30,] -0.021913408  2.067479e-01
#  [31,] -0.018500452  2.073179e-01
#  [32,] -0.015078112  2.078500e-01
#  [33,] -0.011646731  2.083441e-01
#  [34,] -0.008206652  2.088002e-01
#  [35,] -0.004758218  2.092183e-01
#  [36,] -0.001301776  2.095983e-01
#  [37,]  0.002162331  2.099401e-01
#  [38,]  0.005633754  2.102438e-01
#  [39,]  0.009112148  2.105092e-01
#  [40,]  0.012597164  2.107364e-01
#  [41,]  0.016088453  2.109254e-01
#  [42,]  0.019585668  2.110761e-01
#  [43,]  0.023088457  2.111885e-01
#  [44,]  0.026596471  2.112626e-01
#  [45,]  0.030109358  2.112985e-01
#  [46,]  0.033626768  2.112960e-01
#  [47,]  0.037148349  2.112552e-01
#  [48,]  0.040673749  2.111761e-01
#  [49,]  0.044202615  2.110586e-01
#  [50,]  0.047734594  2.109030e-01
#  [51,]  0.051269333  2.107090e-01
#  [52,]  0.054806479  2.104768e-01
#  [53,]  0.058345677  2.102064e-01
#  [54,]  0.061886575  2.098977e-01
#  [55,]  0.065428817  2.095510e-01
#  [56,]  0.068972050  2.091660e-01
#  [57,]  0.072515919  2.087430e-01
#  [58,]  0.076060070  2.082819e-01
#  [59,]  0.079604149  2.077828e-01
#  [60,]  0.083147801  2.072458e-01
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# [598,] -0.198085887  1.065399e-01
# [599,] -0.195817191  1.091583e-01
# [600,] -0.193521379  1.117485e-01
# [601,] -0.191198683  1.143105e-01
# [602,] -0.188849333  1.168438e-01
# [603,] -0.186473564  1.193482e-01
# [604,] -0.184071615  1.218235e-01
# [605,] -0.181643726  1.242695e-01
# [606,] -0.179190139  1.266859e-01
# [607,] -0.176711100  1.290724e-01
# [608,] -0.174206856  1.314288e-01
# [609,] -0.171677658  1.337549e-01
# [610,] -0.169123759  1.360505e-01
# [611,] -0.166545414  1.383152e-01
# [612,] -0.163942882  1.405490e-01
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# [615,] -0.155992772  1.470620e-01
# [616,] -0.153296114  1.491695e-01
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# [628,] -0.119232270  1.718993e-01
# [629,] -0.116260232  1.735744e-01
# 
# $`West-3.03`
#                 [,1]          [,2]
#   [1,]  0.0992973469  0.7070334492
#   [2,]  0.1026709401  0.7082150654
#   [3,]  0.1060605990  0.7093507341
#   [4,]  0.1094659847  0.7104403418
#   [5,]  0.1128867567  0.7114837795
#   [6,]  0.1163225728  0.7124809428
#   [7,]  0.1197730895  0.7134317321
#   [8,]  0.1232379617  0.7143360523
#   [9,]  0.1267168430  0.7151938129
#  [10,]  0.1302093855  0.7160049281
#  [11,]  0.1337152398  0.7167693169
#  [12,]  0.1372340555  0.7174869028
#  [13,]  0.1407654806  0.7181576141
#  [14,]  0.1443091621  0.7187813836
#  [15,]  0.1478647454  0.7193581490
#  [16,]  0.1514318752  0.7198878527
#  [17,]  0.1550101947  0.7203704416
#  [18,]  0.1585993460  0.7208058675
#  [19,]  0.1621989702  0.7211940869
#  [20,]  0.1658087075  0.7215350609
#  [21,]  0.1694281967  0.7218287555
#  [22,]  0.1730570760  0.7220751412
#  [23,]  0.1766949825  0.7222741935
#  [24,]  0.1803415523  0.7224258924
#  [25,]  0.1839964209  0.7225302227
#  [26,]  0.1876592228  0.7225871740
#  [27,]  0.1913295916  0.7225967407
#  [28,]  0.1950071604  0.7225589218
#  [29,]  0.1986915614  0.7224737210
#  [30,]  0.2023824261  0.7223411469
#  [31,]  0.2060793855  0.7221612127
#  [32,]  0.2097820698  0.7219339364
#  [33,]  0.2134901089  0.7216593408
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#  [41,]  0.2433025996  0.7177633667
#  [42,]  0.2470420930  0.7170646994
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#  [46,]  0.2620126123  0.7138024744
#  [47,]  0.2657565073  0.7128704371
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#  [49,]  0.2732431947  0.7108672213
#  [50,]  0.2769852386  0.7097962432
#  [51,]  0.2807259169  0.7086791594
#  [52,]  0.2844648556  0.7075160818
#  [53,]  0.2882016808  0.7063071266
#  [54,]  0.2919360188  0.7050524147
#  [55,]  0.2956674962  0.7037520716
#  [56,]  0.2993957398  0.7024062273
#  [57,]  0.3031203768  0.7010150164
#  [58,]  0.3068410348  0.6995785781
#  [59,]  0.3105573417  0.6980970559
#  [60,]  0.3142689258  0.6965705980
#  [61,]  0.3179754161  0.6949993571
#  [62,]  0.3216764418  0.6933834903
#  [63,]  0.3253716329  0.6917231592
#  [64,]  0.3290606199  0.6900185297
#  [65,]  0.3327430338  0.6882697725
#  [66,]  0.3364185064  0.6864770622
#  [67,]  0.3400866702  0.6846405783
#  [68,]  0.3437471583  0.6827605043
#  [69,]  0.3473996048  0.6808370283
#  [70,]  0.3510436443  0.6788703426
#  [71,]  0.3546789125  0.6768606439
#  [72,]  0.3583050458  0.6748081331
#  [73,]  0.3619216817  0.6727130155
#  [74,]  0.3655284584  0.6705755007
#  [75,]  0.3691250154  0.6683958022
#  [76,]  0.3727109929  0.6661741382
#  [77,]  0.3762860323  0.6639107308
#  [78,]  0.3798497762  0.6616058063
#  [79,]  0.3834018682  0.6592595952
#  [80,]  0.3869419531  0.6568723321
#  [81,]  0.3904696768  0.6544442558
#  [82,]  0.3939846866  0.6519756091
#  [83,]  0.3974866310  0.6494666388
#  [84,]  0.4009751599  0.6469175958
#  [85,]  0.4044499243  0.6443287350
#  [86,]  0.4079105768  0.6417003154
#  [87,]  0.4113567713  0.6390325997
#  [88,]  0.4147881632  0.6363258547
#  [89,]  0.4182044094  0.6335803510
#  [90,]  0.4216051682  0.6307963634
#  [91,]  0.4249900996  0.6279741700
#  [92,]  0.4283588651  0.6251140532
#  [93,]  0.4317111278  0.6222162990
#  [94,]  0.4350465525  0.6192811971
#  [95,]  0.4383648056  0.6163090410
#  [96,]  0.4416655554  0.6133001280
#  [97,]  0.4449484717  0.6102547590
#  [98,]  0.4482132263  0.6071732384
#  [99,]  0.4514594927  0.6040558744
# [100,]  0.4546869462  0.6009029788
# [101,]  0.4578952642  0.5977148668
# [102,]  0.4610841258  0.5944918573
# [103,]  0.4642532121  0.5912342726
# [104,]  0.4674022062  0.5879424383
# [105,]  0.4705307932  0.5846166838
# [106,]  0.4736386602  0.5812573415
# [107,]  0.4767254966  0.5778647474
# [108,]  0.4797909935  0.5744392407
# [109,]  0.4828348444  0.5709811641
# [110,]  0.4858567451  0.5674908632
# [111,]  0.4888563931  0.5639686872
# [112,]  0.4918334887  0.5604149882
# [113,]  0.4947877341  0.5568301217
# [114,]  0.4977188339  0.5532144460
# [115,]  0.5006264950  0.5495683228
# [116,]  0.5035104265  0.5458921166
# [117,]  0.5063703402  0.5421861952
# [118,]  0.5092059500  0.5384509290
# [119,]  0.5120169724  0.5346866916
# [120,]  0.5148031263  0.5308938595
# [121,]  0.5175641330  0.5270728118
# [122,]  0.5202997165  0.5232239307
# [123,]  0.5230096031  0.5193476012
# [124,]  0.5256935220  0.5154442107
# [125,]  0.5283512047  0.5115141497
# [126,]  0.5309823855  0.5075578112
# [127,]  0.5335868013  0.5035755907
# [128,]  0.5361641915  0.4995678865
# [129,]  0.5387142985  0.4955350994
# [130,]  0.5412368672  0.4914776327
# [131,]  0.5437316455  0.4873958920
# [132,]  0.5461983838  0.4832902856
# [133,]  0.5486368355  0.4791612241
# [134,]  0.5510467566  0.4750091202
# [135,]  0.5534279063  0.4708343893
# [136,]  0.5557800464  0.4666374487
# [137,]  0.5581029418  0.4624187183
# [138,]  0.5603963600  0.4581786198
# [139,]  0.5626600718  0.4539175773
# [140,]  0.5648938508  0.4496360168
# [141,]  0.5670974736  0.4453343666
# [142,]  0.5692707199  0.4410130567
# [143,]  0.5714133723  0.4366725193
# [144,]  0.5735252166  0.4323131885
# [145,]  0.5756060416  0.4279355002
# [146,]  0.5776556393  0.4235398921
# [147,]  0.5796738046  0.4191268039
# [148,]  0.5816603357  0.4146966767
# [149,]  0.5836150340  0.4102499537
# [150,]  0.5855377041  0.4057870794
# [151,]  0.5874281536  0.4013085003
# [152,]  0.5892861935  0.3968146640
# [153,]  0.5911116380  0.3923060201
# [154,]  0.5929043047  0.3877830193
# [155,]  0.5946640141  0.3832461140
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# [537,] -0.1040318898  0.4291529667
# [538,] -0.1032914191  0.4335256011
# [539,] -0.1025142866  0.4378797568
# [540,] -0.1017005700  0.4422149983
# [541,] -0.1008503506  0.4465308921
# [542,] -0.0999637136  0.4508270066
# [543,] -0.0990407476  0.4551029122
# [544,] -0.0980815448  0.4593581814
# [545,] -0.0970862012  0.4635923886
# [546,] -0.0960548163  0.4678051103
# [547,] -0.0949874933  0.4719959254
# [548,] -0.0938843389  0.4761644148
# [549,] -0.0927454633  0.4803101615
# [550,] -0.0915709806  0.4844327511
# [551,] -0.0903610081  0.4885317712
# [552,] -0.0891156668  0.4926068120
# [553,] -0.0878350813  0.4966574660
# [554,] -0.0865193797  0.5006833281
# [555,] -0.0851686934  0.5046839957
# [556,] -0.0837831575  0.5086590688
# [557,] -0.0823629107  0.5126081498
# [558,] -0.0809080949  0.5165308439
# [559,] -0.0794188557  0.5204267588
# [560,] -0.0778953419  0.5242955049
# [561,] -0.0763377058  0.5281366953
# [562,] -0.0747461033  0.5319499460
# [563,] -0.0731206936  0.5357348755
# [564,] -0.0714616391  0.5394911054
# [565,] -0.0697691057  0.5432182601
# [566,] -0.0680432627  0.5469159669
# [567,] -0.0662842828  0.5505838560
# [568,] -0.0644923417  0.5542215606
# [569,] -0.0626676187  0.5578287169
# [570,] -0.0608102962  0.5614049643
# [571,] -0.0589205600  0.5649499451
# [572,] -0.0569985991  0.5684633048
# [573,] -0.0550446056  0.5719446921
# [574,] -0.0530587750  0.5753937589
# [575,] -0.0510413058  0.5788101602
# [576,] -0.0489923997  0.5821935544
# [577,] -0.0469122617  0.5855436032
# [578,] -0.0448010998  0.5888599715
# [579,] -0.0426591251  0.5921423278
# [580,] -0.0404865517  0.5953903438
# [581,] -0.0382835970  0.5986036947
# [582,] -0.0360504813  0.6017820592
# [583,] -0.0337874277  0.6049251194
# [584,] -0.0314946627  0.6080325610
# [585,] -0.0291724156  0.6111040734
# [586,] -0.0268209184  0.6141393493
# [587,] -0.0244404065  0.6171380852
# [588,] -0.0220311178  0.6200999812
# [589,] -0.0195932932  0.6230247412
# [590,] -0.0171271766  0.6259120727
# [591,] -0.0146330146  0.6287616870
# [592,] -0.0121110565  0.6315732991
# [593,] -0.0095615546  0.6343466278
# [594,] -0.0069847638  0.6370813958
# [595,] -0.0043809418  0.6397773296
# [596,] -0.0017503490  0.6424341597
# [597,]  0.0009067516  0.6450516204
# [598,]  0.0035900943  0.6476294498
# [599,]  0.0062994107  0.6501673903
# [600,]  0.0090344300  0.6526651881
# [601,]  0.0117948785  0.6551225933
# [602,]  0.0145804803  0.6575393603
# [603,]  0.0173909568  0.6599152473
# [604,]  0.0202260270  0.6622500167
# [605,]  0.0230854073  0.6645434352
# [606,]  0.0259688118  0.6667952733
# [607,]  0.0288759522  0.6690053059
# [608,]  0.0318065378  0.6711733120
# [609,]  0.0347602755  0.6732990747
# [610,]  0.0377368700  0.6753823816
# [611,]  0.0407360235  0.6774230242
# [612,]  0.0437574362  0.6794207985
# [613,]  0.0468008059  0.6813755047
# [614,]  0.0498658284  0.6832869474
# [615,]  0.0529521970  0.6851549354
# [616,]  0.0560596032  0.6869792819
# [617,]  0.0591877362  0.6887598046
# [618,]  0.0623362833  0.6904963252
# [619,]  0.0655049295  0.6921886703
# [620,]  0.0686933580  0.6938366705
# [621,]  0.0719012500  0.6954401610
# [622,]  0.0751282847  0.6969989816
# [623,]  0.0783741393  0.6985129763
# [624,]  0.0816384893  0.6999819937
# [625,]  0.0849210083  0.7014058869
# [626,]  0.0882213680  0.7027845136
# [627,]  0.0915392384  0.7041177358
# [628,]  0.0948742877  0.7054054204
# [629,]  0.0982261823  0.7066474384
kc.examp |> plot()

Measuring fit of CVA

Summary measures for CVA

Rotate and reflect

Zooming in

One dimensional biplots

Three dimensional biplots

biplot(iris) |> CVA(iris[,5],dim.biplot = 3) |> plot()

https://github.com/MuViSU/SASA2024_MDAG